gapt.proofs.epsilon.Epsilon.scala Maven / Gradle / Ivy

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General Architecture for Proof Theory

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package gapt.proofs.epsilon

import gapt.expr._
import gapt.expr.formula.Formula
import gapt.expr.formula.constants.LogicalC
import gapt.expr.ty.->:
import gapt.expr.ty.To
import gapt.expr.ty.Ty

object EpsilonC extends LogicalC("ε") {
  def apply(qtype: Ty) = Const(name, (qtype ->: To) ->: qtype, List(qtype))

  def unapply(e: Expr): Option[Ty] = e match {
    case Const(n, t, ps) => unapply((n, t, ps))
    case _               => None
  }
  def unapply(p: (String, Ty, List[Ty])): Option[Ty] =
    p match {
      case (`name`, (qtype ->: To) ->: qtype_, qtype__ :: Nil) if qtype == qtype_ && qtype_ == qtype__ => Some(qtype)
      case _                                                                                           => None
    }
}

object Epsilon {
  def apply(x: Var, spec: Formula): Expr =
    App(EpsilonC(x.ty), Abs(x, spec))

  def unapply(e: Expr): Option[(Var, Formula)] = e match {
    case App(EpsilonC(_), Abs(x, spec: Formula)) => Some((x, spec))
    case _                                       => None
  }
}